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Long-Wave Perturbation Method to Investigate Nonlinear Stability of the Thin Power Law Liquid Film Flowing Down on a Vertical Cylinder

Published online by Cambridge University Press:  05 May 2011

P. -J. Cheng  and
K. -C. Liu
P. -J. Cheng*
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan, Taiwan 74448, R.O.C.
K. -C. Liu*
Affiliation:
Department of Mechanical Engineering, Far-East University, Tainan, Taiwan 74448, R.O.C.
*
*Associate Professor, corresponding author
**Professor
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Abstract

The influence of both the flow index and the cylinder size on the nonlinear hydrodynamic stability of a thin power law liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weakly nonlinear dynamics of the film flow for stability analysis. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained. The modeling results indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Keywords

Thin filmStability analysisFlow indexPower law liquid.
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 3 , September 2008 , pp. 241 - 252
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

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